Detection and Measurement of Nuclear Radiation (1962)

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details of such a gamma-ray assay chamber, which is filled with 40 atmospheres of dry argon for high gamma-ray efficiency. Sources may be loaded as solids or as liquids in small bottles, which makes the arrangement free of complicated sample- preparation procedures. Because of the high sensitivity of the chamber, it is necessary to enclose it in a 4-in.-thick lead housing as a means of reducing environmental background effects. 6. Energy Spectra In several laboratories, gridded ionization chambers are used routinely for analyzing energy spectra of charged particles, especially alpha particles from radioactive samples. This method has been especially important in research on the trans- uranium elements. Good energy resolution (better than 1%) can be attained with large-area sources; background effects are very low; and the high geometry (nearly 50%) yields a high efficiency. The present "state of the art" has been reviewed 47 by Hanna. Since the advent of the simple, high-resolution semiconductor detectors, many of the favorable arguments for grid chambers have been vitiated; however, the ionization chamber is still useful where both large sources and high geo- metrical efficiency are required. IV. SEMICONDUCTOR RADIATION DETECTORS Basic understanding of the physics of semiconductors has evolved, for the most part, during the years following the invention of the transistor in 1948. The technology of semi- conductor devices has proceeded hand in hand with the advances in basic science, and this combined effort of theorists and technologists has made a significant contribution to the detection and measurement of nuclear radiation. In this section we will discuss the use of p-n junctions and surface barriers as charged-particle detectors, an application which promises to become the most important innovation in radiation detectors since the development of the modern scintillation counter. 58

1. Principles and Description The semiconductor radiation detector behaves quite analo- gously to the gas ionization chamber, except that the charge is carried by electrons and electron vacancies (holes), instead of by electrons and positive ions. Because of this similarity the device is often termed a solid-state ionization chamber. The use of a solid as a detector is very attractive, because the sensitive layer can be very thin and yet possess a high stop- ping power. Another advantage results from the low energy to produce one hole-electron pair (3.5 ev in Si): nearly eight times as much charge is produced for a given energy loss in silicon as in argon gas, which leads to small statistical fluctuations in the number of pairs and improved energy reso- lution over gas-filled counters. The intrinsically high speed of the device is due to the high mobility of the carriers in the electric field, coupled with the short distance between electrodes. A. Introduction to Semiconductor Theory. Except at very low temperatures, a highly purified semiconductor exhibits intrinsic conductivity, as distinct from impurity conductivity of specimens which contain foreign atoms at some of the lattice sites. The electronic band scheme which explains this behavior can be discussed with reference to Fig. 26. At absolute zero the conduction band is vacant, while the valence band is filled. As the temperature is raised, electrons in the valence band are transferred by thermal activation across the energy gap and into the conduction band. Both the vacancies (i.e., holes) in the valence band and the electrons in the conduction band contribute to the electrical conductivity and are called carriers. Apart from the intrinsic method of carrier excitation, electrons and holes may be introduced extrinsically from impurities or imperfections. Consider in particular the effect of impurities on silicon and germanium, which crystallize in the diamond structure with the chemical valence four. If a pentavalent atom such as P, As, or Sb is substituted for a Si For an introduction to the theory of semiconductor radiation detectors, see Brown,48 and for an introduction to semicon- ductor devices in general, see Jonscher,^° Shive,^^ and Henisch.51 59

atom, there will be one valence electron left over. Such a pentavalent impurity is called a donor, because the energy level of the extra electron lies near the energy of the con- duction band (see Fig. 26); at most temperatures there is a CONDUCTION BAND 0.04 0.06 ev JL DONOR IMPURITY LEVELS FORBI G/ 1.11 DDEN \P •V ACCEPTOR IMPURITY LEVELS | VALENCE BAND Fig. 26. Electronic band scheme for silicon. high probability that the electron will be raised into the con- duction band. Since the conductivity in this case is by nega- tive charges, the material is said to be n-type. A trivalent atom such as B, Al, Ga, or In is called an acceptor because it can take on an electron from the valence band, leaving a hole; the resulting conductivity can be ascribed to the motion of the positive holes, and the material is said to be p-type. The Fermi-Dirac probability distribution function gives the probability that a given state is occupied at a particular temperature. The energy about which the probability curve is symmetrical (i.e. , the probability = 1/2) is called the Fermi energy or the Fermi level. Without resorting to a mathematical treatment, it is sufficient to state qualitatively that in a p-type semiconductor, the Fermi level lies in the energy gap, near the valence band; on the other hand, because n-type material contributes a large number of electrons into the con- duction band, the Fermi level is displaced to an energy near the conduction band. The process of stopping a charged particle in a semi- conductor results in lifting electrons from the valence and 60

other low-lying, occupied bands to higher, unoccupied bands. Thus, electrons appear in nominally unoccupied bands, and holes are created in nominally full bands. Interactions between electrons and holes cause the electrons to fall to the lowest available levels in the conduction band, while the holes rise to the highest levels of the valence band. The many states of this process, which are complete in about 10"12 sec, result in an overall expenditure of 3.5 ev to produce one hole-electron pair in Si. It may be noted that this is about three times the 1.1-ev energy gap in Si, which is the minimum energy to produce a hole-electron pair. The additional energy is believed to be lost through strong coupling between electrons and lattice vibrations of the solid. The energy to produce one hole-electron pair in a Si detector is independent of particle type, within the accuracy of existing measurements. This is a notable advantage over the usual Nal(Tl) or CsI(Tl) scintillation spectrometer, for which the light output per Mev of energy transferred to the crystal depends greatly on the ionization density of the heavy particle involved. Recent data on the response of surface barrier and diffused junction diodes to fission fragments does give some evidence for a defect. It is likely that this isolated case of nonproportionality of pulse height with energy involves a failure to collect all the current carriers formed in high density by the intensely ionizing fragments. The reader quite reasonably might ask why detectors are not made from materials with a smaller forbidden gap and hence a smaller energy requirement for producing a hole-electron pair. In general, a material with a small forbidden gap can only be used at low temperatures; otherwise, thermal excitation of carriers will obviate its usefulness. Good low-temperature detectors of Ge(w = 2.9) have indeed been made. B. Production of High Fields in a Semiconductor. It is easy in principle to arrange the solid-state equivalent of a uniform-field, parallel-plate ionization chamber; however, due to the small electrode spacing and the necessity for a high electric field to collect all of the charge, the resistivity of the material must be very high. Even the highest resistivity material passes such a large current that the power dissipation at several thousand volts/cm would reach alarming proportions. More important are the random fluctuations in the current, 61

which would be very large in proportion to the minute signal arising from the collection of hole-electron pairs at the electrodes. Thus, it is necessary to find some other way of sustaining a high electric field inside a solid without the use of high applied voltages and without requiring material of very high resistivity. p-n Junctions. One way in which the necessary field may be obtained is by means of a reversed-biased, p-n junction. This device is fabricated from high-resistivity p-type material (sometimes called 7T-type) , into which a small amount of donor impurity such as phosphorus has been diffused. A high donor density exists in this surface layer which is only a micron or less in thickness. The equilibrium condition for such a situ- ation is shown in Fig. 27(a). The electrons at the n-type surface tend to diffuse to the left, and the holes in the p-type bulk material tend to diffuse to the right. Thus, the p-type region acquires a negative charge and the n-type region becomes positively charged, until the two regions are aligned about the constant Fermi level energy of the system. The result of this equi- librium is that a potential barrier is established which opposes any further flow of electrons or holes across the junction. A space-charge region or depletion layer now exists, in which the acceptors are completely filled and the donors are completely empty. There must be an overall balance of positive and negative charge. Since the density of acceptors is low in the high-resistivity p-type material, the space charge region extends much further into the p-type region than into the n-type layer. The potential difference is about 0.6 volt, and may extend over 10~3 cm. The resulting electric field is not uni- form but averages several hundred volts in Si at room temperature. If a voltage is applied to the junction by connecting the negative terminal to the p-type region and the positive termi- nal to the n-type region, the junction is said to be reverse- biased. As this reverse bias voltage is increased, the barrier height increases and the space-charge region is extended [see Fig. 27(b)]. The exhaustion-layer theory of Schottky53 has been very successful in accounting for the properties of potential barriers and space-charge regions in semiconductors. The nomograph of Fig. 28 is useful for applying the Schottky theory to practical silicon diodes. If the applied bias voltage and the resistivity of the base material (p-type silicon in the 62

ACCEPTOR LEVELS a _ a a a a (a) EQUILIBRIUM . . _ ffl DONOR LEVELS Fig. 27. Band scheme for a p-n junction. E-, represents the energy of the Fermi level; Ep and Ev indicate the lower edge of the conduction band and the upper edge of the valence band, respectively. case just described) are known, the barrier depth x may be quickly determined. Since the depletion layer is the only region containing a high field for collection of charge, the experimenter must be able to estimate x in order to be certain that incident particles will be stopped within the sensitive part of the counter. Note that the nomograph in Fig. 28 includes values for the dynamic capacitance in pf/cm2. This capacitance arises because the space-charge region resembles two charge sheets of finite thickness, separated by a thin, high-resistivity layer, the barrier itself. A modification of the p-n junction detector, which promises to yield sensitive regions deep enough even for beta particles 63

VOLTAGE DEPTH BARRIER CAPACITANCE IMPURITY RESISTIVITY APPLIED X C/cm2 CONCENTRATION /VTYPE PTYPE (v) Kf6 METERS RANGE - 10"12 f N/cm3 ^N PP ENERGY (Mev) 4 — -40,OOO 400- PROTO 12- N ImmllOOO — 900 — -10 5- 6 — jp.ooo - 30,000 -9000 300 — 11 — 10 — 800 — 700- I. 7 — r 8 — — 8000 -7000 — 20,000 9 — 600 — — 6000 — 15,000 200 — 500 — - x10 — 5000 ~ 8 — 400- - — 4000 150 — 7 : i — 10.0OO ~ — it) ^^-^ ~ — 900O - 300- I -- — -"— -3000 — 800O 100 — 6 — -40 -.--"*"" 2- — 700O - 90 — 5— JOO-? —-— " -2000 — 6000 70 — < -60 3- -5000 60 — -.----*-" 4~ —— -— -70 -1500 -40OO Kf\ -80 4- J\J — --""" -90 -3000 40 — 100 — 7 100 5 — -1000 90 — 6 — -900 30 — 80 — ALPHA 70 _ i 8 — -800 -700 -200O 60 — -600 -150O 20 — 9 — 50- 7 x1013 — -500 *J 2 — 8- 40 — -300 1.5^ -400 -1000 -900 7- 30 -f — — -300 -800 10 — - 400 2 -= -700 9 — 8 — 5- "26"-^ -500 -200 -600 7 — - -600 3- — 500 6 — 1 — 4- -700 -150 — 400 5— - — 800 4 — -900 4 — 3- 10- -1000 5 — — 100 w%* 3 — 6 — X2 = .-jlp 1.326 x1015, C/A=1.061x104, 7 •''=7^ cm2/volt-sec, Fp = 450 cm2/volt-sec Fig. 28. Nomograph which relates the applied reverse bias voltage, barrier depth, dynamic capacitance, and impurity concentration for a Schottky-type barrier in silicon. The impurity concentration may be found by using the resistivity in ohm-cm of the base material used. Also included are ranges of charged particles in silicon corresponding to particular barrier depths (Blankenship and Borkowski^) . 64

of several Mev, makes use of the "ion-drift" technique investi- gated by Pell. ' A junction is formed on p-type silicon by diffusing lithium into the surface; the lithium finds its way into interstitial positions and acts as a highly mobile donor. A plot of the donor and acceptor concentrations in the junction are shown in Fig. 29(a). If reverse bias is applied to this junction, the electric field in the region around the point c will exert a force which will move the positively charged Li+ ions from the Li-rich side of the junction to the Li-deficient side. This effect requires that the temperature be sufficiently high to impart appreciable mobility to the Li+ ions. The result of such an ion drift is shown in Fig. 29(b). Over a consider- able region the donor concentration has been adjusted to compen- sate precisely for the acceptor concentration; in effect, a region of intrinsic silicon has been formed. Pell has shown that x2 is approximately proportional to the time of drift at constant temperature and bias voltage. UJ u 15 cc 3 00 Fig. 29. Illustration of the ion-drift technique, (a) Density of donor and acceptor atoms as a function of depth from the surface, after forming the p-n junction. (b) Follow- ing ion drift, the donor concentration equals the acceptor concentration over a significant region (Pell") . Elliott has reported on the fabrication and evaluation of detectors made by ion drift. He was successful in producing detectors with x = 0.338 cm, which corresponds to the range of 96-Mev alpha particles, 24-Mev protons, or 1.7-Mev electrons. A Li-drifted diode having a depletion layer 0.20 cm thick (or an electron range of 1.1 Mev) gave an energy resolution of 2.5% full width at half-maximum at 624 kev electron energy; most of

this width was due to electronic noise. The ion-drift technique therefore appears to be a very promising method for attaining thick depletion layers at room temperature. Surface Barriers. A second general class of semiconductor device which can build up a high electric field for the col- lection of charge is the surface barrier detector, which is usually made from high-resistivity, n-type silicon. Although the detailed mechanism is not well understood, the nature and formation of the surface barrier is believed to arise from surface states, whose existence is well established for silicon and germanium. ' As shown in Fig. 30(a), the surface states are able to trap electrons from the crystal until the Fermi level at the surface is equal to the Fermi level in the interior. The high density of electrons on the surface and the positive charge on the semiconductor which yielded the electrons combine to dis- tort the energy levels E.. and E~ near the surface, and a potential barrier results. The positive space charge within the barrier arises because the donor sites are nearly completely ionized, and there are few if any electrons to compensate. Further, the space charge is enhanced near the surface by the presence of minority carriers (holes). Note that in establish- ing the conditions for a surface barrier, the Fermi level approaches the top of the valence band just as it would for a p-type semiconductor. The region bounded by the surface and r Surface Layer Center of Gap Surface ' States (a) EQUILIBRIUM (b) REVERSE BIASED Fig. 30. Electron-energy-band scheme at the surface of n-type silicon, showing the formation of a surface barrier. Developmental lithium ion-drift detectors are available from Solid State Radiations, Inc., 2261 South Carmelina Avenue, Los Angeles 64, California. 66

the point where the Fermi level crosses the center of the gap is often called an inversion layer, because its properties closely resemble a semiconductor of the type opposite to that of the interior. In a sense, therefore, the inversion layer forms a p-n junction with the bulk material. With reverse bias applied [Fig. 30(b)], the depletion region widens very much as was observed for the p-n junction. In fact, the theoretical treatment used to obtain the nomograph in Fig. 28 does not distinguish between barriers formed at p-n junctions or at surfaces. C. Collection of Charge. Many of the general remarks on the operation of gas ionization chambers apply equally to the semiconductor type as well. It will be recalled that, in gas ionization chambers, the low mobility of heavy positive ions gives rise to several problems associated with the collection of charge; on the other hand, the semiconductor detector possesses the great advantage that both the hole and the electron are highly mobile current carriers. In silicon at room tempera- ture the electron mobility ^n = 1200 cm2/volt-sec and the hole mobility u = 500 cm2/volt-sec. This situation makes it possible to collect all the charge in a short time, regardless of the location of the event within the depletion layer, and so the output pulse height is largely independent of such geo- metrical effects, although the rising portion of the pulse may show some variation in shape. The charge q collected for an average energy E dissipated in the sensitive region is q = e | n , (12) where w is the energy to produce one hole-electron pair (3.5 ev for silicon), and t] is the collection efficiency. In a good diode, it should be possible to increase the bias to the saturation value (to a bias for which 77 = 1) . Even when the bias is sufficient to sustain a depletion layer deep enough to contain the entire charged-particle track, the charge collection still may not be complete. This loss of charge carriers may occur in two ways. First, holes and electrons can be trapped by structural imperfections and chemi- cal impurities which have significant capture cross sections for the current carriers. An electron, for example, may be immobilized at one such location for a period of time and then 67

be released; it may go through this process several times on its way to the positive electrode. The charge collected in such a case will consist of a band of pulses, randomly dis- tributed in time but with an integral of one electronic charge. Fortunately, this effect is usually not large, and so it is unnecessary to use very long clipping times in the amplifier to be certain of complete charge collection from traps. The movement of carriers through the field can also be affected by recombination. The electrons and holes produced along a charged-particle track will drift in opposite directions in the electric field, and so before the two charge clouds separate, they must pass through each other. During this time recombination centers are being exposed to both electrons and holes, and occasionally the conditions are met for the elimi- nation of one hole and one electron at one of these sites. Both trapping and recombination effects depend upon the presence of impurities in the high field region. The most important regions for charge collection are those with high electric fields; in semiconductor detectors the high electric field is at the surface. Unfortunately, the surface region is most likely to contain impurities, especially in p-n junctions formed by high-temperature diffusion. Surface-barrier diodes and junctions formed at low temperature have advantages in this respect. Recombination and trapping effects should be relatively small for work with electrons and most heavy charged particles. However, fission fragments, which produce intense ionization along a very short track, exhibit measurable loss of charge. The loss of charge by recombination and trapping has been 5 Q investigated and reviewed by Miller and Gibson. ' The signal voltage appearing across the detector is readily obtained from the charge q, and the sum of the barrier capacitance C, and the stray capacitance C : V = q/(C, + C ). (13) D S Note that for a strictly proportional relationship between V and q, both C. and C must be constants. 2. Fabrication Techniques Semiconductor radiation detectors resemble conventional photovoltaic cells, and the usual semiconductor fabrication 68

5 9 methods are followed. In this section, emphasis will be given to silicon diodes, because they are suitable for room- temperature operation; however, excellent detectors for oper- ation at liquid-nitrogen or liquid-helium temperatures have been made by using germanium as the base material. A. Diffused Junctions. A typical diffused junction diode is shown in Fig. 31(a). The general procedure to be described here resembles the technique of Donovan. Wafers of p-type silicon are cut to squares 5x5 mm, and about 1 mm thick, using a diamond saw; they are then lapped and etch polished. The heavily doped n+ layer is prepared by phosphorus diffusion. The phosphorus may be introduced by painting a suspension of P2O5 in an organic liquid on the top surface and heating for 10 minutes at 900°C. A more uniform layer, which is also freer from trace impurities, can be diffused by exposure to gaseous P2O5 at 900°C for a few minutes. In both cases, the resulting n+ layers are about 0.1 micron thick. The sensitive area desired is masked by painting with Apiezon W wax dissolved in trichloroethylene. A deep etching is made which removes not only the excess n+ material, but also the p-type substrate to a considerable depth. This leave the so-called "mesa" configuration shown in the figure. Junction edges must be protected from ambient effects either by a covering of wax or an oxide layer. CONTACT WIRE- n* LAYER /• APIEZON "W" L ALUMINUM p-TYPE SILICON ^G22E^ ALLOY DISJUNCTION (p+) CONTACT PLATE GOLD n-TYPE SILICON FILIVK y --~EpOXY * ^/////////J*€^ GUSSEI f:Ji "- • EPOXY-' . ' --'-.DISK : •• . . - - - / - . OK CC (MIC / ""LEAD ELECTRICAL NTACT-^ (a) JUNCTION (b) SURFACE BARRIER Fig. 31. Sketches showing semiconductor radiation detector construction (not to scale). (a) p-n junction detector, (b) Surface barrier detector. A metal contact to the high-resistivity p-type silicon must be carefully designed, otherwise an injecting contact may develop, producing erratic results. One of the simplest contacts is made by amalgamating a metal plate to the silicon with indium amalgam. If a pressure contact is to be used, an alloy junction 69

is made by alloying an acceptor metal such as aluminum with the high-resistivity base. This may be done immediately following the phosphorus diffusion. About 0.05 micron of aluminum is evapo- rated onto the lower face of the wafer, followed by heating to 650°C for a few minutes. This forms a heavily doped, or p+ layer, to which a pressure contact may be made with ease. During the final etching, both the sensitive n+ face and the p+ alloy must be protected by wax. Because of the heavy doping of the n* layer, an ohmic contact to it is readily made. A gold, or even a copper wire is put in pressure contact with the n+ layer. The contact is improved if a 0.01 jafd capacitor, charged to several hundred volts, is discharged through the diode in the forward bias direction. This welding operation is known as "forming," or to the initiated as "zapping" the diode. Junction detectors similar to the design just described may be obtained from several manufacturers. B. Surface Barriers. The surface-barrier detector shown 54 in Fig. 31(b) resembles the design of Blankenship and Borkowski, with some modifications by Chetham-Strode, et al. The wafers of n-type silicon are cut to about 5 x 5 x 1 nun 59 and then lapped. The lapped wafer is nickel plated, and the ohmic contact is made by soldering a wire to the nickel. The solder joint is painted with Apiezon W wax, and the entire crystal is immersed in the etching bath. After the etching is complete, the wafer is laid on an epoxy disk, with the electrical lead protruding through a small hole. Mounting is accomplished by flowing a smooth gusset of epoxy resin around the wafer so that all edges are protected. A thin layer of gold (-100 ^gm/cm2) is then deposited by vacuum evaporation over the entire top face of the assembly, to form a conducting layer. Electrical con- nection to this layer is made by pressure contact to the top face of the epoxy disk. Lower leakage currents and higher Some manufacturers are: Harshaw Chemical Company, 1945 East 97th Street, Cleveland 6, Ohio. Hughes Aircraft Company, P. O. Box 90515, International Airport Station, Los Angeles 45, California. RCA Victor Company, Ltd., Montreal 30 Canada. Solid State Radiations, Inc., 2261 South Carmelina Avenue, Los Angeles 64, California. 70

inverse voltage breakdowns will be obtained if the finished detectors are baked for 48 hours at 110°C. Because of their sensitivity to ambients, surface barrier detectors should be stored in a vacuum dessicator before use. Silicon surface barrier detectors similar to the type just described are available from commercial sources. C. Guard-Ring Detectors. Surface leakage currents at the edge of a semiconductor radiation detector are often much greater than leakage currents through the bulk, and so they constitute an important source of noise. This edge leakage becomes quite serious when it is desired to fabricate detectors of large sensitive area, because the increase of exposed surface area causes an attendant increase in the detector noise. Also, the leakage noise increases with the reverse bias applied, and the noise may limit the usable bias to an unacceptably low value in cases where a deep depletion layer, and hence a high reverse bias, is required. As was mentioned earlier, some form of edge protection is required; various materials have been suggested for this purpose, e.g., Apiezon W, epoxy resins, oxide films, and silica or glass films. A technique which promises to be very useful in some appli- cations is the use of a guard ring, similar in principle to the guard ring of a gas ionization chamber (Section III.4., above). A guard-ring p-n junction detector used by Hansen and Goulding is shown in Fig. 32. The sensitive detector area is the center BIAS VOLTAGE -— SIGNAL OUTPUT n+ LAYER ETCHED RING ' p-TYPE SILICON ETCHED AWAY p* ALLOY LAYER (OHM 1C CONTACT) Fig. 32. Guard-ring details for a p-n junction radiation detector (Hansen and Goulding°z). For example, from Oak Ridge Technical Enterprises Corp. P. O. Box 524, Oak Ridge, Tennessee. 71

disk-shaped region defined by the etched ring. The guard ring formed at the periphery is connected directly to the bias- voltage source; therefore, leakage currents at the edge of the detector flow from the bias supply to ground and do not pass through the load resistor RT. Since the potentials of the it guard ring and center disk differ only by the amount of the signal voltage, leakage across the etched ring is extremely small. For best results, however, good surface treatments must be used on all etched surfaces. Prototype versions of guard-ring p-n junction detectors are now available commercially. 3. Application to Spectrometry A. Electronics. A typical electronic system for use with a silicon surface barrier detector is sketched in Fig. 33. The bias supply must be well filtered, and it is usually helpful to monitor the leakage current and the rms noise as the bias voltage is varied. TEST PULSE GENERATOR — i „* INCIDENT b CHARGE SENSITIVE PREAMP. MAIN AMPLIFIER PULSE HEIGHT ANALYZER PARTICLES P~| | .. r4_| -L-^S < • 0.1 10 M / LOW \ T * < M LEAKAGE; -=- Fig. 33. Functional block diagram of equipment used with a surface-barrier detector. Because signals from the detector are of such low ampli- tude, the preamplifier should be very carefully designed for low input noise. It is also recommended that the preamplifier be of the "charge-sensitive" type (Section VI.2.D., below), Solid State Radiations, Inc., 2261 South Carmelina Avenue, Los Angeles 64, California. 72

which produces an output pulse whose amplitude is proportional to charge and not voltage. A voltage-sensitive amplifier will reflect any variations in the input capacitance resulting from variations in the barrier properties (cf., Eq. 13); such irregular changes in capacitance can occur but are not serious if the amplifier is charge sensitive. A test-pulse generator with low-impedance output may be used for checking the operation of the system. When used as shown in Fig. 33, the generator may be calibrated in terms of energy and will, for a given generator amplitude setting deliver the same amount of charge to the preamplifier even though the input capacitance may vary greatly. Its output is a useful substitute for a detector pulse. The noise of the system with an equivalent capacitance substituted for the detector may be measured by injecting an amount of charge corresponding to some given energy, and from the width of the peak obtained the amplifier noise may be calculated. The equivalent noise from such a measurement typically is 3-10 kev full-width at half- maximum. The clipping time of the main amplifier may be chosen for optimum signal to noise ratio, since the collection time is extremely rapid compared to gas ionization chambers. Recommended 54 clipping times are 0.5 to 2 ^sec. If the sensitive depth is determined with particles of known energy, it is found that the measured depth exceeds the value of x obtained from Fig. 28. Further, the experimental value increases with an increase in the clipping time. This behavior arises because the electron-hole pairs created outside the space charge region do not contribute to the current immedi- ately. They diffuse about in the field-free region and may reach the edge of the space-charge region, where one of the carriers will be swept across and collected. Since this is a slow process compared with the normal collection of charge formed within the field, the probability of collecting charge by diffusion is enhanced by slowing down the amplifier response. Naturally, this is an artifact and is of no practical importance if the space- charge region always extends beyond the incident particle range. B. Experimental Arrangement. Semiconductor detectors have been applied to the study of many types of charged parti- cles. Perhaps the most successful application of interest to chemists is in high-resolution alpha spectroscopy, although 73

Al~ PLATE BAKELITE CU ELECTRODE H.V. Fig. 34. Exploded view of a chamber for study of alpha- particle spectra with a surface-barrier detector (Chatham-Strode, et al.61). recent advances in technique indicate that these detectors may eventually find even more widespread use in electron and beta- ray energy studies. Figure 34 shows the counting chamber designed by Chetham-Strode, et al., for precision alpha spectrometry with silicon surface-barrier detectors. The relatively large internal dimensions were chosen to remove scattering surfaces from the source and detector. The detector was recessed so that the sensitive part of the detector could not "see" the scattering surfaces. Since the surface-barrier detector is rather sensitive to air ambients, and the alpha-particle energy is degraded by air, provision was made for evacuating the chamber. 74